Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics C

COMMUTATIVE PROPERTIES OF OPERATORS IN SCHWINGER B000N REPRESENTATION

Heng Fan

Published Jan 1, 1986• 0 citations
OpenAlex

Abstract

The angular momentum theory in the schwinger boson representation is developedto derive a new normal product expression for the commutator [e~(iαJx), e~(iβJy] by meansof the integral technique within normal product, and the effect on the coherent statecaused by two rotations which are in different seqences. Some new normal productexpressions for exponential operators, sueh as e~(σJ)-e~(λJ)+ etc, are also derived and theirapplications in atomic coherent states are presented.

Related papers

Normal Product Expansion of Rotation Operators Gained by Coherent State Method

Fan Hang-yi

In Schwinger boson representation of angular momentum theory we derive new normal product expansion of rotation operators which can generate new operator identities in the Hilbert space to which SU 2 group maps, some properties and applications of them are presented.

Communications in Theoretical Physics•Mar 1, 1987•6 citations

New Approach to the Study of Atomic Coherent State

Fan Hong‐Yi

On the basis of the technique of performing integration within ordered product proposed in our previous paper [1] and Schwinger boson representation for angular momentum, we derive new normal product forms for coset element of group and their product as well as some new operator identities which are useful in studying atomic coherent state. This new formulation provides the possibility of making use of the Glauber coherent state to find new properties of atomic system.

Communications in Theoretical Physics•Dec 1, 1987•2 citations

New Operator Identities Gained via Coherent State Formulation

Fan Hong-Yi, Ruan Tu-Nan

By the properties of the coherent state and the technique of performing integrations within ordered products as in Ref. [1], we derive some new useful operator ordering identities. Their applications, especially in studying the Boglyubov transformations both in one and two dimensional cases, are presented. The explicit non-unitary operators which turn the coordinate or momentum eigen-state to the corresponding coherent state are also given. Moreover, by using the Schwinger angular momentum theory and the technique mentioned above we find the normal product form of the rotation operator, with which the coefficient of the rotation D-matrix can be easily obtained.

Communications in Theoretical Physics•Mar 1, 1985•16 citations

Feynman Transformation Matrix Element for a type of Hamiltonian of Angular Momentum system

Hong-Yi Fan

Using the technique of integration within ordered product (IWOP) of operators and the Schwinger boson representation for the angular momentum theory as well as the coherent state's method, we evaluate the Feynman transformation matrix element for the angular momentum system whose Hamiltonian is (A, B, C real). The eigenstate of H is derived and the comparison between it and the coherent state is made.

Communications in Theoretical Physics•Mar 1, 1992•1 citation

Schwinger Boson Representation for the Quantized Rotator

M. Yamamura, T. Suzuki, H. Ichihashi

Schwinger representation for angular momentum operators is extended to that for the quantized rotator by introducing four kinds of bosons. The basis vectors and fundamental operators of the quantized rotators are expressed in the closed forms with respect to the boson operators.

Progress of Theoretical Physics•Jul 1, 1978•7 citations

Properties and Applications of the Intermediate Coordinate-momentum Representation

MA Mei-juan

The state |x〉λ,v was derived by using the technique of integration within an ordered product of operators(IWOP)that was the eigenstate of two rotational quadrature components λQ^+vP of light field.The basic vector |x〉λ,v becomes a new quantum mechanics representation which is between coordinate representation and momentum representation.With the help of the new representation,we obtain the normal product of the operators exp[-f(λQ +vP )2] and(λQ+vP)n.Furthermore,we construct a new quantum unitary operator which is used on vacuum state can obtain a new quantum optics squeezing state.

Jilin Normal University Journal•Jan 1, 2011•0 citations
The angular momentum theory in the schwinger boson representation is developedto derive a new normal product expression for the commutator [e~(iαJx), e~(iβJy] by meansof the integral technique within normal product, and the effect on the coherent statecaused by two rotations which are in different seqences. Some new normal productexpressions for exponential operators, sueh as e~(σJ)-e~(λJ)+ etc, are also derived and theirapplications in atomic coherent states are presented.
By the properties of the coherent state and the technique of performing integrations within ordered products as in Ref. [1], we derive some new useful operator ordering identities. Their applications, especially in studying the Boglyubov transformations both in one and two dimensional cases, are presented. The explicit non-unitary operators which turn the coordinate or momentum eigen-state to the corresponding coherent state are also given. Moreover, by using the Schwinger angular momentum theory and the technique mentioned above we find the normal product form of the rotation operator, with which the coefficient of the rotation D-matrix can be easily obtained.
The state |x〉λ,v was derived by using the technique of integration within an ordered product of operators(IWOP)that was the eigenstate of two rotational quadrature components λQ^+vP of light field.The basic vector |x〉λ,v becomes a new quantum mechanics representation which is between coordinate representation and momentum representation.With the help of the new representation,we obtain the normal product of the operators exp[-f(λQ +vP )2] and(λQ+vP)n.Furthermore,we construct a new quantum unitary operator which is used on vacuum state can obtain a new quantum optics squeezing state.